Diagnostic Test Pattern Generation
and Fault Simulation for Stuck-at and
Transition Faults
Committee:
Vishwani D. Agrawal
Adit Singh
University Reader:
Sanjeev Baskiyar, CSSE
Victor P. Nelson
Bogdan M. Wilamowski
Student:
Yu Zhang
Auburn University, Auburn, Alabama 36849 USA
Mar. 21, 2012
Zhang: PhD Defense
1
Purpose
• Identification of fault is useful in the
characterization phase of design.
• Present ATPG tools emphasize only
fault detection.
• There is an accepted measure for fault
detection coverage but none for
diagnostic coverage.
• Diagnosis must deal with non-classical
faults, not just single stuck-at faults.
Mar. 21, 2012
Zhang: PhD Defense
2
Outline
• Purpose (motivation)
• Introduction & Background
• Diagnostic ATPG System
– Diagnostic Fault Simulation
– Exclusive Test Generation
– Equivalence Identification
• Exclusive test for transition fault
• Experimental results
• Conclusion
Mar. 21, 2012
Zhang: PhD Defense
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Diagnostic ATPG Problem
• Given a circuit and a fault model, find:
– Test vectors to distinguish between all, or
most, fault-pairs.
– Measure diagnostic coverage of vectors.
• Present contributions:
– A new diagnostic coverage metric.
– A diagnostic ATPG system using new algorithms
and conventional stuck-at fault detection tools.
– A diagnostic ATPG system for transition faults using
new algorithms and available fault-detection tools
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Introduction
Basic testing flow.
Test
Patterns/
Vectors
---00
---01
---11
--- ---- ---- ----10
Stored
expected
output
response
Circuit under Test
(CUT)
Output
Responses
Comparator
Mismatch
Faulty
Circuit
Mar. 21, 2012
10--01---- ---- ---- --11---
Match
Good
Circuit
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Fault Detection and Diagnosis
1
Fault
D
0
CUT
Fault
D
1
• Fault detection: Need at least one vector that detects
a target fault.
• Fault diagnosis: Need at least one vector that
produced different responses for every pair of faults.
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Introduction*
Fault detection test generation:
Find an input vector such that faulty response
differs from fault-free response.
C0  C1 = 1
Detection
test vector
CUT with
fault f1
C1
sa0
Fault free
CUT
C0
* Yu Zhang, V. D. Agrawal, “A Diagnostic Test Generation
System,” in Proc. International Test Conf., Nov 2010.
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Introduction
Exclusive test:
A test that detects only one Simplified:
fault from a fault-pair.
(C0  C1)  (C0  C2) = 1
Exclusive
test vector
Exclusive
test vector
CUT with
fault f1
C1
⇒
CUT with
Fault free
faultC0f1
CUT
CUT with
fault f2
C1  C2 = 1
C1
C2
CUT with
fault
f2
C2
Fault free
CUT
Mar. 21, 2012
sa0
sa0
C0
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Diagnostic Test Generation System
Conventional ATPG
1. Structurally
collapsed
fault set
2. ATPG system
for detection
fault coverage
Functionally
equivalent fault-pair
No
Undiagnosed
fault-pair
Adequate
diagnostic
coverage?
Yes
Mar. 21, 2012
4. Exclusive test
generator
Detection
vectors
Exclusive
vectors
Test
vectors
3. Diagnostic
fault simulator
Stop
Diagnostic
ATPG
Zhang: PhD Defense
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Diagnostic Fault Simulator*
• Given a set of vectors and a set of
faults, find:
– Diagnostic coverage
– Identify undiagnosed fault groups with two
or more faults
– Eliminate the need to target all n(n – 1)/2
fault pairs
* Y. Zhang and V. D. Agrawal, “An Algorithm for Diagnostic Fault
Simulation,” Proc. 11th IEEE Latin-American Workshop, March 2010.
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Diagnostic Fault Simulation
1. For an input test vector find detected faults.
2. Group faults with same syndrome (detection
pattern at primary outputs).
3. Calculate/update diagnostic coverage (DC).
4. Continue steps 1 through 3 with next test vector
until no vectors left.
Mar. 21, 2012
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Diagnostic Fault Simulation
Original
fault set
Simulate t1
G0
Simulate
t2
G0
fa
G4
G3
G2
G2
G5
fb
G7
Simulate t3
Simulate tn
Mar. 21, 2012
fc
fd
fe
Zhang: PhD Defense
G5
12
Diagnostic Fault Coverage (DC)*
• Diagnostic coverage (new)
• Fault coverage (conventional),
Where g0 is the set of undetected faults.
* Yu Zhang, V. D. Agrawal, “A Diagnostic Test Generation System and a
Coverage Metric,” 15th IEEE European Test Symp., May 2010.
Mar. 21, 2012
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DC vs. Fault-Pair Coverage – C432
1.1
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1000
900
800
700
600
500
400
300
DC
200
Distin. FP/Total FP
100
No. of Un. FP
1
11
21
31
41
0
51
61
Number of Undistinguished
Fault Pairs
Coverage as fraction
Diagnostic Coverage
Number of ATPG Vectors
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Diagnostic Fault Simulation
Take ISCAS85 benchmark
circuit c17 as an example:
1
10
3
20
2
16
5
6
14
11
15
7
Mar. 21, 2012
22
Zhang: PhD Defense
21
23
19
15
Diagnostic Fault Simulation
• 22 collapsed fault in c17 (f1~f22):
f1: 22 sa1
f2: 10 sa1
f3: 22 sa0
f4: 16->22 sa1
f5: 3->10 sa1
f6: 1 sa1
f7: 3 sa0
f8: 3 sa1
f9: 16 sa1
f10: 16 sa0
f11: 11->16 sa1
Mar. 21, 2012
f12:
f13:
f14:
f15:
f16:
f17:
f18:
f19:
f20:
f21:
f22:
Zhang: PhD Defense
2 sa1
11 sa0
3->11 sa1
11 sa1
6 sa1
23 sa1
19 sa1
23 sa0
16->23 sa1
11->19 sa1
7 sa1
16
Diagnostic Fault Simulation
Test vector set for c17 (generated by
our diagnostic ATPG system):
t1:
t2:
t3:
t4:
t5:
t6:
t7:
t8:
00000
10110
11101
01110
10011
00111
11000
01010
Mar. 21, 2012
00
10
11
00
01
00
11
11
1
10
3
2
6
22
20
14
5
11
7
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16
21
19
23
17
Diagnostic Fault Simulation
Fault simulation without fault dropping:
test 1: 00000 00
f1: * 10
f2: 00
Fault free
f3: 00
response
f4: 00
for test 1
f5: 00
f6: 00
* indicates
f7: 00
detected faults
f8: 00
f9: 00
f10: * 11
f11: 00
Mar. 21, 2012
Zhang: PhD Defense
f12:
f13:
f14:
f15:
f16:
f17:
f18:
f19:
f20:
f21:
f22:
* 11
00
00
00
00
* 01
00
00
00
00
* 01
18
Diagnostic Fault Simulation
Faults can be grouped according to
syndromes (syndromes of t1):
Groups
Faults
Syndrome
t1
G1
f1
10
G2
f10,f12
11
G3
f17,f22
01
G0
All other faults
00
In syndrome, ‘1’ represents a mismatch with
fault free response. ‘0’ means match.
f1 will be dropped from further simulation.
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Diagnostic Fault Simulation
Mar. 21, 2012
Groups
Faults
Syndrome
t1
G1
f1
10
G2
f10,f12
11
G3
f17,f22
01
G0
All other faults
00
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Diagnostic Fault Simulation
Fault simulation with t2:
test 2: 10110
G2: f10: * 11
f12: 10
G3: f17: * 11
f22: 10
Mar. 21, 2012
G0: f2: * 00
f3: * 00
f4: 10
f5: 10
10
f6: 10
f7: * 00
Fault free
f8: 10
response
f9: 10
f11: 10
f13: 10
G0 contains
f14: 10
undetected
f15: 10
faults.
f16: 10
After test2 f2, f3,
f18: 10
and f7 will leave
f19: 10
G0.
f20: 10
f21: 10
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Diagnostic Fault Simulation
After applying t2:
Groups
G2
G4
G3
G5
G0
G6
Faults
Syndrome
t2
f10
01
f12
00
f17
01
f22
00
All other faults
00
f2, f3, f7
10
f10, f12, f17, f22 are dropped from
further simulation
Mar. 21, 2012
Zhang: PhD Defense
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Diagnostic Fault Simulation
Groups
G2
G4
G3
G5
G0
G6
Mar. 21, 2012
Faults
Syndrome
t2
f10
01
f12
00
f17
01
f22
00
All other faults
00
f2, f3, f7
10
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Dictionary Construction
This is a fault dictionary constructed after
applying t2.
It can be used for cause-effect diagnosis
‘X’ means don’t care or unknown
Faults
Syndrome
t1
Syndrome
t1
Syndrome
t3 ~ t8
f1
10
X
…
f10
11
01
…
f12
11
00
…
f17
01
01
…
f22
01
00
…
f2, f3, f7
00
10
…
All other faults
00
00
…
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Diagnostic Fault Simulation
Continue to apply test vectors to all groups,
and divide faults into sub groups.
After t1:
f1 is dropped
G1:
f1 (10)
G2:
f10, f12 (11)
G0:
f1, f2, f3,…f22
(no test applied) G0:
G3:
All other
f17, f22 (01)
faults (00)
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Diagnostic Fault Simulation
After t2:
G2:
f10, f12
G2:
f10 (01)
G5:
f12 (00)
Single fault groups
are dropped.
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Diagnostic Fault Simulation
Similarly for G3:
G3:
f17, f22
G3:
f17 (01)
G6:
f22 (00)
Single fault groups
are dropped.
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Diagnostic Fault Simulation
For G0:
G0:
f2~f9, f11, f13~f16,
f18~f21
G7:
f2, f3, f7
(10)
Mar. 21, 2012
No faults are
dropped hereG0:
all other
undetected
faults (00)
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Diagnostic Fault Simulation
• For c17 after applying all 8 test vectors, we
get 22 fault groups with only one fault in each
group.
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Fault Dropping
• Each group contains faults that are not
distinguished from others within that group,
but are distinguished from those in other
groups.
• During simulation once a fault is placed alone
in a single-fault group, it is dropped from
further simulation.
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Diagnostic Fault Simulation
Summarize:
Original
fault set
Simulate t1
G0
Simulate
t2
G0
fa
G4
G3
G2
G2
G5
fb
G7
Simulate t3
Simulate tn
Mar. 21, 2012
fc
fd
fe
Zhang: PhD Defense
G5
31
Summary for Fault Simulation
• Diagnostic coverage metric defined.
• Diagnostic fault simulation has similar
complexity as conventional simulation with
fault dropping.
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Exclusive Test* Generation
• An exclusive test for fault-pair (f1, f2)
distinguishes between the two faults.
• If no exclusive test exists, then the two faults
cannot be distinguished from each other and
form an equivalent fault-pair.
* V. D. Agrawal, D. H. Baik, Y. C. Kim, and K. K. Saluja,
“Exclusive Test and its Applications to Fault Diagnosis,” Proc.
16th International Conf. VLSI Design, Jan. 2003, pp. 143–
148.
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Exclusive Test Generation
Need two copies of circuit
New
model:model:
Previous
Exclusive
Exclusive
testtest
vector
vector
X
Sa0 or Sa1
y
Mar. 21, 2012
C1  C2 = 1
C1
C1
CUT
with
CUT with
fault
fault f1
f1
sa0
0
CUT with
with
CUT
fault f2
f2
fault
C2
C2
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1
G(X,y)
34
Exclusive Test Generation
Single circuit copy ATPG: find a test vector to
distinguish fault f1 (line x1 s-a-a) from fault f2 (line x2 s-a-b)
PO
PI
line x1
line x2
Mar. 21, 2012
s-a-a
s-a-b
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New Diagnostic ATPG Model
• Two-copy ATPG model with C1 and C2:
• Substitue:
• Single-copy ATPG model with C:
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Single Copy Exclusive Test Generation
Consider exclusive test for x1 s-a-a and x2 s-a-b
y
PO
x1
PI
x1’
a
x2
CUT C
Mar. 21, 2012
G
x2’
b
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A Simplified Model
Suppose a is 0 and b is 1, the model can be simplified:
y
x1
x1’
PO
PI
x2’
x2
CUT C
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Exclusive Test Generation Example
ISCAS85 c17 benchmark circuit:
1
10
3
sa0
20
2
22
16
5
6
14
11
15
7
21
23
19
sa1
t1: 00000 00
t2: 10110 10
Mar. 21, 2012
Seven test vectors
generated by ATPG; 100%
fault coverage but some
fault-pairs not distinguished
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Exclusive Test Generation
1
0
0
1
1
6
0
10
3
20
2
22
1/0
16
14
11
21
15
19
23
7
y
Sa0 or Sa1
Mar. 21, 2012
t8: 10010 00
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0/1
Advantages of Exclusive Test Algorithm
• Reduced complexity: Single-copy ATPG
model is no more complex than a single fault
ATPG.
• No need for especially designed diagnostic
ATPG tools that try to propagate different
logic values of two faults to POs.
• Can take advantage of various existing fault
detection ATPG algorithms.
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Experimental Results
Detection test Generation
Circuit
No. of
faults
c17
Diagnostic test Generation
Det.
Vect.
FC
%
CPU
s*
DC
%
Excl. Abort Equv.
Vect. pairs pairs
DC
%
CPU
s*
22
7
100.0
0.03
95.5
1
0
0
100.0
0.03
c432
524
51
99.2
0.03
92.0
18
13
13
100.0
0.03
c499
758
53
100.0
0.03
97.4
0
12
12
100.0
0.03
c880
942
60
100.0
0.05
92.6
10
55
55
100.0
0.05
c1355
1574
85
100.0
0.05
58.9
2
740
740
100.0
0.13
c1908
1879
114
99.9
0.05
84.7
20
300
277
98.8
0.07
c2670
2747
107
98.8
0.11
79.1
43
494
466
98.9
0.34
c3540
3428
145
100.0
0.13
85.2
29
541
486
97.2
0.42
c6288
7744
29
99.6
0.22
85.3
108
842
977
99.5
7.60
c7552
7550
209
98.3
0.39
86.0
87
904
1091
99.4
2.18
* Core 2 Duo 2.66GHz 3GB RAM
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Need for Equivalence Identification
• Some fault-pairs are functionally equivalent; not found in
structural collapsing.
• Exclusive test ATPG may leave many undiagnosed fault
pairs as aborted faults.
• Many techniques have been proposed for fault
equivalence identification:
– Structural analysis
– Exhaustive enumeration
– Learning & implication
– Branch & bound
– Circuit transformation & symmetry identification
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Equivalence Identification*
sa1
Extract a small logic block
Faults are functionally equivalent if,
exclusive test impossible,
or faulty circuits identical.
Dominator gate
for both faults
sa0
* M. E. Amyeen, W. K. Fuchs, I. Pomeranz, and V. Boppana, “Fault Equivalence
Identification in Combinational Circuits Using Implication and Evaluation
Techniques,” IEEE Transactions on Computer-Aided Design of Integrated Circuits
and Systems, vol. 22, no. 7, Jul. 2003.
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Summary of Test Generation
• New diagnostic test generation algorithm
uses conventional tools:
– Diagnostic fault simulation drops diagnosed
faults; similar complexity to conventional
fault simulators.
– Exclusive test generation requires only
single fault detection.
– Fault equivalence checking is important for
DC; requires effective algorithm.
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Exclusive Test Gen. For Tran. Faults
• Introduction and background
• Representing a transition fault as a single
stuck-at fault
• Exclusive test patterns for transition faults
– One and two time frame models
• Experimental Results
• Summary
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Purpose
• Many modern design failures behave as
non-classical faults.
• Most failures are timing related.
• Transition fault model is widely used
due to its simplicity.
• There exist a need for diagnosis using
the transition fault model.
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Problem Statement and Contribution
• Modeling and test generation for transition faults:
– Detection of single transition faults
– Exclusive tests for fault-pairs
• Contribution:
– A diagnostic ATPG system for transition faults
using conventional fault-detection tools.
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Examples of Transition Fault *
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Transition Fault Test with Scan
Combinational
Logic
Scan out
SFF
Scan enable
SFF
Scan in
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Two Time-Frame Model
• There are 2 possible ways to model a transition fault
with a single stuck-at fault:
– First, since most digital designs are sequential,
we can use a 2-time-frame circuit.
PI
PO
line x1
line x1
1st time frame
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2nd time frame
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Detection Test Generation
Detection test for xx’ slow-to-rise
Useful for equivalence identification
Two-time-frame Model (Simplified):
PI
PO
x
x
x’
x’
y
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s-a-1
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Representation of a Transition Fault
1
0
Clock
Slow to rise
x’
x
MFF Model:
x
x’
MFF
init. 1
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x
x’
00
00
01
00
10
10
11
11
53
Detection Test Generation
Using MFF Model:
PI
x
0
1
MFF
init. 1
x’
PO
s-a-1
y
Test for y sa1 is also a
test for xx’ slow to rise
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Detection Test Generation
PI
x
x’
PO
MFF
init. 1
s-a-1
y
Test for y sa1 is also a
test for xx’ slow to rise
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Single Copy Exclusive Test Generation
Exclusive test for x1x1’ slow-to-fall and x2x2’ slow-to-rise:
PO
PI
0
1
x1
MFF
init. 0
y
s-a-0/1
Mar. 21, 2012
x2
MFF
init. 1
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0
1
x 1’
x 2’
56
Single Copy Exclusive Test Generation
Simplified version:
PO
PI
x1
MFF
init. 0
s-a-0/1
x2
Mar. 21, 2012
MFF
init. 1
Zhang: PhD Defense
x 1’
x 2’
57
DC vs. Fault-Pair Coverage – s27
Coverage as fraction
1.2
50
45
1
40
35
0.8
30
0.6
25
20
0.4
DC
15
0.2
Distin. FP/Total FP
10
No. of Un. FP
5
0
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Number of Undistinguished
Fault Pairs
Diagnostic Coverage
Number of ATPG Vectors
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Experimental Results
Detection test Generation
Circuit
No. of
faults
s27
Diagnostic test Generation
Det.
Vect.
FC
%
UnFlt
Grp
DC
%
Excl.
Vect.
46
11
100.0
12
52.2
18
1
2
97.8
s298
482
44
79.9
62
62.4
34
39
4
70.1
s382
616
51
80.8
82
64.1
24
58
4
68.5
s1423
2364
102
92.9
280
79.3
106
182
5
84.1
s5378
6589
205
91.2
400
82.0
472
85
7
90.0
s9234
10416
377
92.8
1219
75.8
597
754
8
82.1
s13207
14600
480
89.1
1707
70.0
543
1392
11
74.1
s15850
17517
306
87.6
1961
71.2
486
1565
7
74.3
s35932
52988
75
99.0
3737
88.3
725
2867
4
90.2
s38417
47888
244
98.4
4090
87.5
1336
2883
8
91.0
s38584
56226
395
95.7
4042
86.7
1793
2440
7
90.3
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UnFlt Large
Grp st Grp
DC
%
59
Experimental Results
• Results compared to a recent work*
Detection test Generation
s38584
No. of
faults
Diagnostic test Generation
Det.
Vect.
FC
%
UnFlt
DC
%
1000
2120
--
14197
97.16*
583
This work 56226
395
95.7
4042
86.7
1793
Previous
Excl.
UnFlt
Vect.
DC
%
CPUs
12881
97.42*
174649
2440
90.3
14841
* Y. Higami, Y. Kurose, S. Ohno, H. Yamaoka, H. Takahashi, Y. Takamatsu, Y.
Shimizu, and T. Aikyo, “Diagnostic Test Generation for Transition Faults Using a
Stuck-at ATPG Tool,” in Proc. International Test Conf., 2009. Paper 16.3.
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Future Work
• Implement 2-time frame model to get higher
DC.
• Targeting mixed/multiple fault models.
• Test set compaction using DATPG and
diagnostic fault simulation:
– E.g. reverse/random order simulation of
generated vector set, if no new faults are
detected AND no new fault groups are formed,
the vector in simulation can be dropped.
– Combined with ILP for further compaction.
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Future Work
• Example of exclusive test generation for a stuck-at fault and a
bridging fault:
a
b
d
e
c
a
a’
0
1
1
d
b
c1
1
y
Mar. 21, 2012
1
0
s-a-0
e’
e
c’
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Future Work
Fault dictionary for previous
example:
Test Syndrome
Faults
010
011
100
110
111
a sa0
0
0
0
1
0
a sa1
1
0
0
0
0
b sa1
0
0
1
0
0
c sa0
0
1
0
0
0
c sa1
1
0
1
0
0
e sa0
AND bridge
(a, c)
0
1
0
1
1
0
1
0
1
0
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Summary
• A diagnostic coverage metric is proposed.
• A new diagnostic ATPG system for stuck-at
fault is constructed.
• Experimental results show their effectiveness.
• Extend the DATPG system for transition fault.
• Experimental results show improved DC.
• Only conventional tools are used.
Mar. 21, 2012
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References for Some Figures Used
• Acknowledgement:
* http://courses.ece.uiuc.edu/ece543/docs/
DelayFault_6_per_page.pdf (Slide 49)
* http://www.sciencephoto.com/media/347881/
enlarge (Slide 47)
* http://www.ami.ac.uk/courses/topics/0268_wb/
index.html (Slide 47)
* http://materials.usask.ca/images/photos/SEM6LevelCuChipP98.GIF (Slide 2)
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Publications
•
Y. Zhang and V. D. Agrawal, “Reduced complexity test generation algorithms for transition fault
diagnosis,” in International Conference on Computer Design (ICCD), Oct. 2011, pp. 96 -101.
•
Y. Zhang and V. D. Agrawal, “A Diagnostic Test Generation System,” in Proc. International
Test Conf., 2010. Paper 12.3.
•
Y. Zhang and V. D. Agrawal, “Diagnostic Test Generation and Fault Simulation Algorithms for
Transition Faults” in Proc. 20th North Atlantic Test Workshop, May, 2011
•
Y. Zhang and V. D. Agrawal, “An Algorithm for Diagnostic Fault Simulation,” in Proc. 11th IEEE
Latin-American Workshop, 2010.
•
Y. Zhang and V. D. Agrawal, “A Diagnostic Test Generation System,” in Proc. 19th North
Atlantic Test Workshop, May, 2010.
•
Y. Zhang and V. D. Agrawal, “A Diagnostic Test Generation System and a Coverage Metric,” in
15th IEEE European Test Symp., May 2010.
•
Y. Zhang and V. D. Agrawal, “On Diagnostic Test Generation for Stuck-at Faults,” in
preparation.
•
Y. Zhang and V. D. Agrawal, “A Diagnostic ATPG System Targeting Multiple/Mixed Fault
Models,” in preparation.
Mar. 21, 2012
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Mar. 21, 2012
Zhang: PhD Defense
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